Wave-optical structure design with the local plane-interface approximation

Pfeil, Albrecht von; Wyrowski, Frank

doi:10.1080/09500340008230517

Cited by 28 publications

(11 citation statements)

References 19 publications

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“…We have found that singularities, because of zeros of P D z 1 U in in (14), typically are not a problem in practice.…”

Section: Amplitude Matching Strategymentioning

confidence: 95%

“…although index or surface modulations in dielectrics typically also introduce amplitude modulations if TEA is not a valid structure design method [17,11,14]. Nevertheless, consideration of phase-only operators is reasonable at least as an initial design for the functional embodiment.…”

Section: …4 †mentioning

confidence: 97%

“…Before we turn to the phase-only constraint we would like to state the amplitude matching concept for a general t c distribution in R 2 . More general amplitude constraints may be of interest in combination with other structure design methods other than TEA [14].…”

Section: Amplitude Matching Strategymentioning

confidence: 98%

“…t c in R 2 . According to (14) this condition requires the satisfaction of the amplitude matching condition…”

Section: Amplitude Matching Strategymentioning

confidence: 98%

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Amplitude matching strategy for wave-optical design of monofunctional systems

Schimmel

Wyrowski

2000

Journal of Modern Optics

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The design of optical systems capable of transforming one given input ® eld into an output ® eld which maximizes one prescribed merit function is discussed in the functional embodiment of the system, that is by dealing with transmission functions instead of structured matter. Customary beam shaping techniques are identi® ed as a special case of a more general strategy which is called amplitude matching. This strategy makes use of the ® eld quantities amplitude and phase and therefore it is a wave-optical design approach. Thē exibility of the technique is demonstrated by various examples. Parameters like conversion eae ciency, signal-to-noise ratio, distances between transmission functions, and the number of transmission functions necessary for the implementation of wave transformations are discussed. IntroductionMost optical systems are designed to transport and transform a set of waves in a homogeneous dielectric input region into another set of waves in a homogeneous dielectric output region. The waves in the output region must satisfy prescribed quality criteria. In the following we apply some restrictions to this very general situation. (1) The refractive index in the input and output regions obeys nˆ1.(2) Monochromatic and coherent waves are assumed. (3) We consider only one scalar component U of the electromagnetic ® eld. The general vectorial case may be understood as a two channel generalization of the strategy described below, as long as the system response on both independent scalar components is decoupled, that is for instance a polarization conversion does not occur. (4) The monofunctional case is addressed, that is the system is designed to transform one speci® ed input wave into an output wave which satis® es one prescribed merit function. (5) The structure of the system is mathematically speci® ed by the refractive index of a linear, isotropic and inhomogeneous dielectric, that is n…x ; y ; z †, in a region z in µ z µ z out . By restriction to a dielectric we avoid absorption eå ects and emphasize the transmission mode of operation. The re¯ection mode of operation may be considered analogously. The xy planes through z in and z out indicate the input and output planes of the system.According to the spectrum of plane waves representation (e.g. see [1] section 3.2) the input wave U in …x ; y ; z µ z in † and the output wave U out …x ; y ; z ¶ z out † are completely speci® ed by the ® elds U inˆUin …x ; y ; z in † and U outˆUout …x ; y ; z out † respectively. Thus, in what follows we consider the input and output ® elds U in and U out .

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“…We have found that singularities, because of zeros of P D z 1 U in in (14), typically are not a problem in practice.…”

Section: Amplitude Matching Strategymentioning

confidence: 95%

Section: …4 †mentioning

confidence: 97%

Section: Amplitude Matching Strategymentioning

confidence: 98%

“…t c in R 2 . According to (14) this condition requires the satisfaction of the amplitude matching condition…”

Section: Amplitude Matching Strategymentioning

confidence: 98%

See 2 more Smart Citations

Amplitude matching strategy for wave-optical design of monofunctional systems

Schimmel

Wyrowski

2000

Journal of Modern Optics

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“…This provides further support to our expectation that the primary reason for the early failure of the thin-element approximation in the non-paraxial domain is boundary di raction at the abrupt transitions in the pro le. The results of the perturbation approach could probably be improved further by involving considerations such as those presented in [8] where refraction at the analogue boundary is considered locally. However, such considerations are beyond the scope of this paper.…”

Section: Comparison With Rigorous DI Raction Theorymentioning

confidence: 97%

Step-discontinuity approach for non-paraxial diffractive optics

Vallius

Kettunen

Kuittinen

et al. 2001

Journal of Modern Optics

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An approximate method based on local eld perturbations caused by abrupt transitions of the surface pro le is described, which enables rapid approximate calculation of di raction patterns of di ractive elements in the non-paraxial domain of di ractive optics. In this domain the simple complexamplitude transmittance model based on scalar di raction theory is no longer valid and rigorous computations are exceedingly time-consuming. Comparisons with rigorous di raction theory show that the method is accurate for binary and multilevel pro les provided that the minimum feature size is larger than approximately one optical wavelength. The method is applied to the evaluation of the uniformity error of binary, four-level, and analogue array illuminators. IntroductionIt has become customary to divide the domain of di ractive optics into two subdomains according to the analysis methods involved, even though any such division is necessarily an oversimpli cation [1]. If all features in the surface-relief pro le are much larger than the optical wavelength ¶ and the optical signal generated by the element is therefore of paraxial nature, one speaks of the paraxial domain and makes use of the well-known complex-amplitude transmittance approach to model and design di ractive elements. If, on the other hand, wavelength-scale features are present in the di ractive structure and the signal is non-paraxial, one speaks of the non-paraxial domain and resorts to rigorous di raction theory. In the paraxial domain the modelling and design are relatively simple tasks, but in the non-paraxial domain major computational di culties are faced in a large majority of problems [2]. Therefore methods, which are more accurate than the complex-amplitude transmittance approach but computationally less demanding than implementations of rigorous di raction theory are of considerable value. In this paper we consider in detail one such method, which we introduced recently in a somewhat di erent and less stable form [3].The idea that major contributions to the di raction pattern of an aperture in an opaque screen arise at the sharp material discontinuities at the edges of the aperture is not new: both the Maggi-Rubinowich boundary di raction wave theory and the rigorous theory of di raction by the edge of a perfectly conducting screen describe the di racted eld as a superposition of a geometrical wave and a wave generated at the edge [4]. Considering more general di ractive elements, in

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